The Celtic duo limped out of last week’s friendly against Bristol City and the manager admits they face a “pretty significant” period of rehab.
He couldn’t set an exact timeframe for their return, but said it will be more than a month before either player returns to the pitch.
Postecoglou has signed Liel Abada and will rely on James Forrest, but remains short of attacking options in large areas, with new addition Kyogo Furuhashi having to wait before he can join the Celtic squad.
And now he’ll have to go without Dembele and Johnstone for a while.
Postecoglou said: “We had an early diagnosis, but they both suffered pretty significant injuries and will be out for a while.
These are the kind of players I like to have on the team.
“We don’t want to delay it, but it won’t be less than a month. How much time left? We are awaiting advice.
“It’s disappointing for both.
“I was looking forward to working with them because they are exciting wingers, the kind of players I like to have on the team.
“Unfortunately, this game in Bristol has really cost us, no one to blame. One was a bad tackle and the other a trivial event.
“It’s a big blow and they have quite a lot of rehabilitation ahead of them.
“They have youth and time for them, so I hope they work hard and come back. “
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